Extension theorem for nonlocal operators

Krzysztof Bogdan, Tomasz Grzywny, Katarzyna Pietruska-Pałuba, Artur Rutkowski

Published 2017-10-16Version 1

We solve the extension problem in Sobolev spaces for nonlocal operators under minimal regularity of the exterior values. The extension with the smallest value of the quadratic form is given by a suitable Poisson integral and is the weak solution of the corresponding Dirichlet problem. We express the Sobolev form of the extension as a weighted Sobolev form of the exterior data.